Types
Liquid fuel camp stoves are available in single-burner backpacking stoves and large two-burner tabletop camp stoves. Propane stoves are available as single-burner backpacking stoves, integrated stove systems like Jetboil, and two-burner stoves.
Efficiency
Liquid fuel stoves outperform propane stoves, especially in colder weather. Propane stoves are less efficient when they are low on fuel, whereas liquid stoves perform well down to the last drop of fuel.
Weight
Propane backpacking stoves tend to be lighter in weight than liquid fuel stoves. Two-burner camp stoves are around the same weight regardless of fuel type.
Safety
Propane canister stoves are easier to use than liquid fuel stoves. Liquid fuel stoves need to be primed in order to light so they require some fiddling with an unstable flame.
Environmental Impact
Propane fuel canisters are disposable and can be difficult to recycle. According to REI, liquid fuel stoves create less waste and have less environmental impact.